Durham and Chapel Hill are the closest day trips — both part of the Research Triangle and each worth a half-day. Durham's American Tobacco Campus and the Nasher Museum of Art at Duke University are good targets. Chapel Hill has the University of North Carolina's campus and a walkable downtown.
Further afield, the Outer Banks are about three hours east and worth a dedicated trip for the barrier islands, lighthouses, and the Wright Brothers National Memorial at Kitty Hawk. The Smoky Mountains are four hours west.